Ndukwe, I. E., Shchukina, A., Zorin, V., Cobas, C., Kazimierczuk, K.,& Butts, C. P. (2017). Enabling Fast Pseudo-2D NMR SpectralAcquisition for Broadband Homonuclear Decoupling: The EXACTNMR Approach. ChemPhysChem, 18(15), 2081–2087.https://doi.org/10.1002/cphc.201700474

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FULL PAPER

Enabling fast Pseudo-2D NMR Acquisition for Broadband 1

Homonuclear Decoupling – The EXACT NMR approach 2

I. E. Ndukwe,[a,b] A. Shchukina,[c,d] V. Zorin,[e] C. Cobas,[e] K. Kazimierczuk,*[c] and C. P. Butts*[a] 3

Dedication ((optional)) 4

Abstract: Pseudo-2D NMR provides a means of acquiring broadband

homonuclear decoupled spectra useful for structural characterization

of complex molecules. However, data points concatenated in the

direct dimension in these experiments are acquired over incremented

time periods – leading to long acquisition times with no sensitivity

benefits due to the absence of signal averaging between scans.

Herein, the concept of EXACT NMR (‘burst’ non-uniform sampling of

data points) is explored in pseudo-2D experiments with results

revealing little or no loss in spectral quality or signal intensity despite

the acceleration of acquisition – up to 400% in some cases.

Introduction

Just over a decade ago, Candès and co-workers[1] and Donoho[2]

developed a theoretical basis for compressed sensing – a set of

methods that allow the acceleration of measurement of signals

having compressible representation. In their review of

compressed sensing,[3] Candès and Wakin further expressed the

idea that the “information rate of a continuous time signal may be

much smaller than suggested by its bandwidth”. In effect, under-

sampling such signals – that is sampling at a slower rate than that

required by the Nyquist-Shannon theory[4] – can provide enough

information to define the frequencies within the signals. This finds

application in multi-dimensional NMR spectroscopy where

advancement in alternative (‘non-Fourier’ based) methods of data

analysis and processing, provide more rapid access to higher

dimensionality data in what is known as non-uniform sampling

(NUS) and a myriad of spectrum reconstruction algorithms have

been implemented.[5,6] Recently, we have demonstrated that

“burst” non-uniform sampling and reconstruction approaches can

be leveraged in the direct dimension of NMR experiments,[7]

achieving higher resolution in ‘pure-shift’ experiments that are

limited by the excision of the J-refocussing periods (during which

homonuclear and/or heteronuclear decoupling pulses are

applied[8–14]) or to reduce the high duty cycle and sample heating

associated with broadband heteronuclear decoupling during

acquisition.[15] This application of NUS in the direct dimension is

termed EXACT (EXtended ACquisition Time) NMR spectroscopy.

Pseudo two-dimensional (2D) NMR methods have become

especially important recently in generating broadband homo-

decoupled NMR spectra, exemplified by the Zangger-Sterk (ZS)

slice-selective[16,17] and PSYCHE[18] pure-shift methodologies.

These approaches are distinguished from traditional 2D homo-

decoupled experiments, such as PSYCHE-TOCSY,[19] where the

decoupling elements are built into the t1 evolution periods – giving

rise to a spectrum decoupled in the indirect dimension – and as a

result no significant time penalty is observed. In these methods,

decoupling in the direct dimension is achieved by covariance

NMR spectroscopy[20–23] – a processing scheme that employs the

covariance matrix of a series of 1D spectra to establish nuclear

spin connectivity as per 2D experiments.

In pseudo-2D NMR experiments, the final FID is a one-

dimensional interferogram generated by concatenation of data

points or datachunks acquired over separate incremented time

periods. Such approaches require a long experiment time,

equivalent to that of a regular 2D NMR acquisition, but offer

significant resolution benefits over ‘real-time’ single scan

methods[8–14] – by avoiding the inherent line broadening

accompanying the excision of the J-refocussing periods (unless

aforementioned ‘burst’ non-uniform sampling reconstruction is

applied). In view of the advantages of pseudo-2D experiments

over real-time single-scan pure-shift methods, there are clear

benefits to any scheme that reduces their acquisition time without

compromising the quality of the spectrum acquired.

Herein, we demonstrate that the EXACT NMR concept can be

applied to pseudo-2D acquisition of broadband homonuclear

decoupled NMR spectra, offering substantial time savings in ZS-

1D[16,17] and PSYCHE[18] pseudo-2D experiments without

significant loss in spectral quality, resolution or most importantly

signal intensity.

The EXACT PSYCHE sequence (Figure 1) and EXACT Zangger-

Stark sequences (Figure S2 and Figure S3) are similar to the

original sequences published[16–18] but with non-uniform sampling

[a] Dr. I. E. Ndukwe, Dr., C. P. Butts

Department of Chemistry

University of Bristol

Cantocks Close, Bristol. BS8 1TS. UK.

E-mail: craig.butts@bristol.ac.uk

[b] Dr. I. E. Ndukwe

Department of Pure and Industrial Chemistry

Abia State University, Uturu

PMB 2000. Abia State. Nigeria

[c] Dr. A. Shchukina, Dr. K. Kazimierczuk

Centre of New Technologies

University of Warsaw

Banacha 2C, 02089, Warszawa, Poland.

E-mail: k.kazimierczuk@cent.uw.edu.pl

[d] Dr. A. Shchukina

Institute for Spectroscopy

Russian Academy of Sciences

Fizicheskaya 5, 142190, Moscow, Troitsk, Russia

[e] Dr. V. Zorin, Dr. C. Cobas

Mestrelab Research S.L.

Feliciano Barrera 9B – Bajo, 15706 Santiago de Compostela, Spain

Supporting information for this article is given via a link at the end of

the document.((Please delete this text if not appropriate))

mailto:craig.butts@bristol.ac.ukmailto:k.kazimierczuk@cent.uw.edu.pl

FULL PAPER

Figure 1. The PSYCHE sequence with incorporation of the EXACT acquisition

as described in the text of this work. Unfilled and filled boxes are 90º and 180º

pulses, respectively, while trapezoids are 20% smoothed chirp pulses (30ms

total duration) of low flip angle applied in opposite sweeps (indicated by the

arrows within the trapezoids) during a weak gradient, G0 (1 %). The other

gradients are G1 (49 %) and G2 (77 %) – each of 1ms duration. The phase cycle

is; ϕ1 = 4(x,-x), ϕ2 = 8(x), ϕ3 = 2(x), 2(y), 2(-x), 2(-y), ϕ4 = 2(x, -x, -x, x). The ZS-

1D sequence and variant can be found in the SI.

of the t1 points implemented as follows,

𝑡1 = {𝑗∆𝑇 | 𝑗 ∈ 𝐽𝑝} 1

where,

∆𝑇 = 1 𝑆𝑊1 ≈ 10 − 20𝑚𝑠⁄ 2

𝐽𝑃 ⊆ {0, 1, 2, . . . . . , 𝑛 − 1} 3

Here p represents the sampling density (number of elements in

the list, Jp), j the selected element in JP and n the number of

datachunks acquired. The number of datachunks (n) acquired is

equal to the ratio of the total number of points in the final

interferogram or FID (including points of zero intensity, ntotal) and

the number of points collected per chunk, nchunk i.e. n = ntotal/nchunk.

Note that the first and last chunks (0 and n – 1) are always

acquired. SW1 is set to at least twice the widest multiplet width in

the 1H NMR spectrum to ensure effective decoupling and is

related to the desired final spectrum width, SW by equation 4;[24]

1 𝑆𝑊1⁄ = 𝑛𝑐ℎ𝑢𝑛𝑘 𝑆𝑊⁄ 4

The general scheme for EXACT pseudo-2D acquisition is

illustrated in Figure 2. In the ZS-1D and PSYCHE pseudo-2D

acquisition, datachunks acquired over t1 increments (Figure 2a)

are concatenated to give the full FID (Figure 2c). The EXACT

pseudo-2D experiment is however acquired in significantly less

time by acquiring only a subset of t1 increments, i.e. selected Jp

values (Figure 2b). Datachunks not acquired can be considered

as points of zero intensity such that the acquired data points

exactly match those that would be acquired in the fully sampled

FID (compare Figure 2c and Figure 2d). The missing data points

in the EXACT FIDs can then be reconstructed with existing

algorithms, for example maximum entropy reconstruction[25,26] or

iterative soft thresholding (IST)[27,28] to provide the complete 1-

dimensional FID.

Figure 2. Schematic of (A) Pseudo-2D acquisition and (B) EXACT pseudo-2D acquisition (note that datachunks selected are a function of t1 and are not in a regular

pattern as shown in the figure) with their respective FIDs – (C) and (D) – comprising concatenated data chunks which are acquired over t1 incremented time period.

Pseudo-2D

acquisition EXACT pseudo-2D

acquisition

Concatenation Concatenation

A B

C D

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Results and Discussion

To illustrate the potential of the EXACT approach to pseudo-2D

acquisition, the EXACT PSYCHE sequence (Figure 1) was

acquired at 100%, 50%, 37.5% and 25% sampling density from a

total of 32 t1 increments (each datachunk – 20ms long, Jp values

are shown in SI, Table S1), on a 15mg sample of cyclosporine-A

dissolved in 0.5ml deuterated benzene. Each spectrum was

reconstructed, using IST-based algorithms as reported

previously,[7,15] to 3200 points and then zero-filled to 64K

(excluding the 100% sampled dataset which was Fourier

transformed and then zero-filled to 64K).

The standard (100%) cyclosporine-A PSYCHE spectrum (Figure

3a show zoomed region of Figure S4c), was acquired for

approximately 3 minutes. As only a small statistical percentage of

active spins are observed in the PSYCHE experiment, there is a

substantial loss of sensitivity compared to the 1H spectrum,[18] but

a high quality of homodecoupling is achieved with linewidths of

1.7 - 2.5Hz. The corresponding EXACT PSYCHE acquisitions

with 50%, 37.5% and 25% sampling densities (Figures 3b-d also

show zoomed regions of Figures S4d-f respectively) provide

grossly similar homonuclear decoupling quality but in 1.5, 1.1 and

0.78 minutes respectively. Closer inspection of the homo-

decoupled spectra shows that IST essentially perfectly

reconstructs the 50% sampled EXACT PSYCHE dataset (Figure

3a vs Figure 3b) and that there are only minute differences

apparent in the 37.5% sampled spectrum (Figure 3c). However,

in the reconstructed 25% EXACT dataset (Figure 3d) peak

distortions and reconstruction artefacts in the baseline are clearly

visible, suggesting limitations with the existing IST algorithms

used here.

The key benefit of the EXACT approach to pseudo-2D acquisition

is that the experiment is acquired faster, but with no loss of signal

intensity. This is demonstrated by the absolute peak intensities

shown inset in Figures 3a-d. For example, the peak at 0.65ppm

gave absolute intensities of 2675, 2723, 2684 and 2680

respectively for the 100%, 50%, 37.5% and 25% sampled

PSYCHE spectra (Figures 3a, 3b, 3c and 3d, respectively) –

showing essentially no change in intensity. In fact across all

regions of the spectra, peak intensities varied by no more than

5% between the 100, 50 and 37.5% PSYCHE datasets (see

Figure 3. Zoom of a cross-section (0.55 – 0.85ppm) of the PSYCHE and EXACT PSYCHE cyclosporine-A spectrum showing inset the absolute peak integral (not

signal:noise ratio which cannot be reliably defined for IST-processed spectra) of two equivalent peaks in each spectra of (A) Fully sampled PSYCHE, (B) 50%

sampled EXACT PSYCHE, (C) 37.5% EXACT PSYCHE and (D) 25% EXACT PSYCHE dataset. The 1H NMR of cyclosporine-A is shown in the SI (Figure S4a)..

PSYCHE 100% EXACT PSYCHE 50%

2675 2723

EXACT PSYCHE 37.5% EXACT PSYCHE 25%

2684 2680

2749

2740

2704

2671

A B

C D

FULL PAPER

Tables S2 – S4). However, the 25% sampled PSYCHE spectrum

(Table S5) showed greater variability which is attributed to the

imperfect reconstruction of peakshapes and baseline by the IST

algorithm used (see highlighted region with residual side-bands in

Figure 3d). This retention of signal intensity appears reasonable

as in principle the intensity of a peak is a function of the amplitude

of the first data point in the FID. In the EXACT approach, the

measured data points are not changed by the reconstruction

algorithm – meaning that the peak intensities are fixed in the first

measured datachunk of the spectrum. The consequence of this is

that a well-reconstructed EXACT PSYCHE spectrum has the

same quantitative value as the parent PSYCHE spectrum, but

acquired in substantially shorter time. The signal intensity could

be enhanced by using relaxation-matched NUS[29] where the

sampling scheme emphasizes the measurement of more

datachunks near the beginning of the FID and fewer near the end

of the FID – where signal-to-noise ratio is lower.

An alternative way to consider the benefit of NUS in pseudo-2D

experiments is to compare the resolution which can be obtained

in comparable time. This is shown here in a time-equivalent

comparison between the IST reconstructed 37.5% EXACT

PSYCHE spectrum (i.e. 12 randomly distributed datachunks

totalling 1200 data points, followed by IST-reconstruction of the

missing data points in the gaps, to a total of 3200 – Figure 4a) and

the spectrum from a fully sampled but truncated PSYCHE

experiment, that is 12 consecutive datachunks totalling 1200 data

points (linear predicted to 3200 data points – Figure 4b). In the

EXACT PSYCHE spectrum (Figure 4c), the four peaks in the

highlighted region can be clearly identified while the truncated

PSYCHE spectrum (Figure 4d) lacks the needed resolution to

reveal these peaks, even after linear prediction (LP) of the

acquired data points. This reflects the added stability to the

recovery of the missing data points provided by interpolation using

IST in comparison to extrapolation by LP. An extensive study by

Stern et al[30] on Maximum Entropy method (a similar algorithm to

IST) and linear prediction extrapolation has shown that the former

approach provides more accurate results than the latter – more

so at low signal-to-noise ratios. IST also does not require an

assumption of the number of components in the signal as does

LP and the large number of components in one-dimensional NMR

Figure 4. (A) 37.5% EXACT PSYCHE spectrum with 1200 actual data points acquired (but distributed randomly in chunks as described in this work) and

reconstructed with IST (300 iterations) to 3200 data points and then zero-filled to 64K. (B) The truncated PSYCHE Fourier transform spectra of 1200 consecutive

data points after linear prediction to 3200 data points and zero-filling to 64K. Both spectra of approximately equal experimental time (1.1 minutes), were processed

EXACT PSYCHE 37.5% PSYCHE truncated A B

C D

FULL PAPER

with a 0.1 exponential window function and the respective zoom of the highlighted regions shown in (C) and (D). The highlighted portions (blue in C and D) show

the difference in the resolution achieved.

Figure 5. Zoom of a cross-section (1.98 – 2.65ppm) of (a) the 100% sampled ZS-1D Fourier transformed spectrum and (b) the 25% sampled EXACT ZS-1D IST

reconstructed spectrum of a 136.29mM CDCl3 solution of progesterone. Inset are the absolute peak integrals of three equivalent peaks in both spectra. Please note

that values shown in boxes are peak integrals – which can be used as a measure of signal intensities – and should not be confused with signal-to-noise ratios.

spectra makes the use of the latter generally ineffective. In

addition, LP presumes a pure exponential signal model, which

further limits its use, while IST is generally more insensitive to the

signal model.

The same outcomes are observed with the EXACT modification

of the Zangger-Sterk pseudo-2D experiment (Figure S5). The ZS-

1D spectrum of progesterone (Figure S5c) was acquired with

6,400 data points (64 datachunks) in 24 minutes (8 scans). The

corresponding IST reconstructed EXACT ZS-1D spectra acquired

ZS-1D 100% EXACT ZS-1D 25%

3127 2154 3142 2984 2107

3040

A B

FULL PAPER

Figure 6. (a) The spectrum of the sensitivity enhanced ZS-1D (ZS-1D_multislice) experiment – 100% sampled (2.67 minutes acquisition time) and (b) the IST

reconstructed 37.5% sampled EXACT ZS-1D_multislice variant (1.23 minutes acquisition time) acquired on a 15mg cyclosporine-A sample dissolved in 0.5ml

benzene-D6. Insets are zoom of 5.5 – 8.3ppm region, highlighting the perfect reconstruction of weak peaks in the presence of a strong solvent signal.

at 50, 37.5 and 25% sampling densities (that is 32, 24 and 16

datachunks) in 12, 8 and 6 minutes respectively are shown in

Figures S5d, S5e and S5f. Again, the signal intensities of the

EXACT ZS-1D slice-selective experiments were equivalent to the

parent 100% ZS-1D experiment, even for the 25% EXACT ZS-1D

dataset, where signal intensity losses were < 7% in most cases.

This is exemplified by the 1.98 – 2.65ppm region of progesterone

shown in Figure 5. The singlet resonances at 2.54, 2.28 and

2.04ppm gave similar peak integrals in both the fully sampled ZS-

1D (2154, 3142 and 3127) and the 25% sampled EXACT ZS-1D

(2107, 3040 and 2984) spectra with differences attributed to

imperfect baseline in the former and/or the presence of

reconstruction artefacts in the latter. This is clearly seen in Figure

S6 where both spectra were superimposed and all peaks showed

excellent fitting in linewidths and peak heights – even for weak

peaks – with the only difference between both spectra being the

baseline concatenation and reconstruction artefacts of the ZS-1D

and EXACT ZS-1D datasets respectively.

The sensitivity enhanced ZS-1D[16] (ZS-1D_multislice) sequence

of Figure S3 speeds-up the acquisition of the parent ZS-1D pure-

shift experiment by reducing the recycle delay between

increments to ~ 100ms in addition to the acquisition of only the

required number of data points per t1 increment – that is the

number of points in each datachunk (t2 acquisition time is ~ 1.64s

in the latter whereas it is ~ 0.12s in the former). In this sequence,

fresh magnetization, from previous ‘unperturbed’ slices, is

accessed by moving the offsets of the selective 90ᴼ and 180ᴼ

pulses between increments (see list of offsets in the caption of

Figure S3). The selective pulses’ offsets are iterated such that the

excitation bands at successive offsets do not overlap – providing

ample time for used magnetization to relax. The sensitivity

enhanced ZS-1D sequence ensures that unused magnetization

(that is magnetization outside the selected regions) returns to the

+z – axis at the end of the sequence by the use of a pair of 180ᴼ

Broadband Inversion Pulses (BIP). The ZS-1D_multislice

experiment can now be acquired around four times faster than the

original sequence.[17]

The EXACT approach to pseudo-2D acquisition, as described

herein, is applied to the sensitivity enhanced ZS-1D sequence.

Figure 6 shows comparative spectra acquired with the ZS-

1D_multislice sequence (Figure S3) at 100% sampling density

(Figure 6a, 2 minutes and 40 seconds) and at 50% sampling

density (Figure 6b, 1 minute and 14 seconds) after FT and IST

processing respectively (see SI for the 37.5% spectra). Key

highlight of this methodology is shown inset as weak peaks were

correctly reconstructed, even in the presence of the strong solvent

signal. Peak integrals of the 100 and 50% ZS-1D_multislice

datasets (Table S10 – S11) reveal only small differences in signal

intensity (

FULL PAPER

Conclusions

In conclusion, EXACT pseudo-2D acquisition provides a means

of acquiring homo-decoupled spectra of complex molecules much

more rapidly, with little or no loss in signal intensity, resolution or

peakshape. The correct homo-decoupled spectra of the test

molecules, cyclosporine-A and progesterone, were perfectly

recovered in all cases from the 50% sampled EXACT pseudo-2D

datasets while a good homo-decoupled spectrum could be

obtained for progesterone with sampling as low as 25% –

representing four-times acceleration in speed of acquisition –

using existing IST reconstruction algorithms. This highlights the

key role played by the complexity of the homo-decoupled

spectrum with respect to the number of data points needed for

recovery of the correct spectrum. The experiment time thus

gained can be leveraged to improve the notoriously low sensitivity

of these pseudo-2D methods. Partial randomization of the sizes

(lengths) and sampling distribution of data points within each

datachunk, and gaps as well as improved reconstruction

algorithms for burst-sampled datasets will further aid the recovery

of the correct spectrum from lower sampled datasets.

Experimental Section

Test samples used in this work include; a 128.16mM strychnine sample

(30mg/0.7ml CDCl3), a 274.25mM menthol sample (30mg/0.7ml CDCl3), a

136.29mM progesterone sample (30mg/0.7ml CDCl3) and/or a 24.95mM

cyclosporine-A sample (15mg/0.5ml C6D6). Experiments were acquired on

a Bruker Avance III 500 MHz spectrometer equipped with a 5mm Bruker

two-channel DCH cryoprobe and all experiments were acquired at 25°C.

The spectral widths were set to 5000Hz (SW) and 50Hz (SW1)

respectively for the direct and indirect (pseudo) dimensions for all

experiments. Acquisition parameters for the EXACT PSYCHE and ZS

sequences are listed in the captions of the individual sequences and

experiments were acquired with 2 scans and 8 scans per t1 increment

respectively with a relaxation delay of 0.5s for PSYCHE and ZS-1D

experiments and 0.1s for sensitivity enhanced ZS-1D variant. Missing data

points corresponding to the un-acquired t1 increments in these

experiments were reconstructed with IST algorithm[27,28] implemented in

the mddnmr 2.4 package (see www.mddnmr.spektrino.com) and can be

downloaded here; http://nmr.cent.uw.edu.pl/index.php/download/category/5-pure-shift. This

version was adapted to processing 1D datasets by a Python wrapper

written by Alexandra Shchukina and Krzysztof Kazimierczuk (co-authors

of this manuscript), where virtual echo[31] option was included. The

concatenation and IST reconstruction of the 1D FIDs from the acquired

pseudo-2D datasets is now supported in Mestrenova processing software,

courtesy Vadim Zorin and Carlos Cobas (also co-authors of manuscript).

Acknowledgements

Craig Butts and Ikenna Ndukwe acknowledge the Tertiary

Education Trust Fund, Nigeria for sponsoring Ikenna Ndukwe;

Kzrysztof Kazimierczuk and Alexandra Shchukina thank the

National Science Centre of Poland for SONATA BIS

(2012/07/E/ST4/01386) and OPUS (2015/17/B/ST4/04221)

grants.

Keywords: EXACT • Pure Shift • Non-uniform Sampling •

Pseudo-2D acquisition • Homonuclear decoupling

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http://www.mddnmr.spektrino.com/http://nmr.cent.uw.edu.pl/index.php/download/category/5-pure-shift

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Pseudo-2D experiments are now

acquired at significantly less time with

no loss in spectral quality or signal

intensity.

I. E. Ndukwe, A. Shchukina, Vadim

Zorin, Carlos Cobas, K. Kazimierczuk,*

and C. P. Butts*

Page No. – Page No.

Enabling fast Pseudo-2D NMR

Acquisition for Broadband

Homonuclear Decoupling – The

EXACT NMR approach

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Text for Table of Contents

Author(s), Corresponding Author(s)*

Page No. – Page No.

Title

2.7 MINUTESPseudo-2D acquisition

1.2 MINUTESEXACT Pseudo-2D acquisition

Half the time – Equal Intensity

0 1 2 3 4 5 6 7 8 9

FTIST

reconstruction

247191 241193

0 1 2 3 4 5 6 7 8 9

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